Markovian Two Server Single Vacation Queue with Heterogeneous Arrival and Service Rates

Abstract

customers in the system at a service completion point. The inter-arrival times and the service times follows negative exponential distributions and the arrival rates depends on the server’s state. Each arriving customer requires exactly one server for its service. On arrival, if the customer finds one server free he enters in to that server for service or if the customer finds both the server free he selects the server using random selection or if the customer finds both servers busy he waits for the a server become free. The queue discipline is FCFS. The vacation period follows negative exponential distribution. For this model, the steady state results have been obtained. Some performance measures have been calculated and numerical models are given.